Complex Systems

Exponential Period of Neuronal Recurrence Automata with Excitatory Memory Download PDF

René Ndoundam
Electronic mail address: ndoundam@uycdc.uninet.cm.

Maurice Tchuente
Electronic mail address: tchuente@camnet.cm.
Department of Computer Science,
Faculty of Science, University of Yaounde I,
P.O. Box 812 Yaounde, Cameroon

Abstract

The sequences generated by a neuronal recurrence equation with memory of the form x ( n ) = 1 [ i = 1 h a i x ( n - i ) - θ ] , where h is the size of the memory, are studied. It is shown that in the case where all the parameters ( a i ) 1 i h are positive reals, there exists a neuronal recurrence equation of memory length h that generates a sequence of period Ω ( e h ( ln ( h ) ) 2 3 ) . This result shows that in the case where all the weighting coefficients are positive reals, the neuronal recurrence equation exhibits a complex behavior.